ECON 3818

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# ECON 3818
## Chapter 1
### Kyle Butts
### 10 August 2021

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## Introduction

---
# What to expect from the course
	
.subheader.coral[Objectives:]
- Give you a background on statistical theory and their application

- Learn how to perform basic statistical analysis in the .mono[R] programming language

- Prepare you to succeed in econometrics courses

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    </tr>
    
  </thead>
  <thead class="gt_col_headings">
    <tr>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">Assignment</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Percentage</th>
    </tr>
  </thead>
  <tbody class="gt_table_body">
    <tr><td class="gt_row gt_left">Homework</td>
<td class="gt_row gt_right">10%</td></tr>
    <tr><td class="gt_row gt_left">R Problem Sets</td>
<td class="gt_row gt_right">10%</td></tr>
    <tr><td class="gt_row gt_left">R Project</td>
<td class="gt_row gt_right">10%</td></tr>
    <tr><td class="gt_row gt_left">Midterm 1</td>
<td class="gt_row gt_right">20%</td></tr>
    <tr><td class="gt_row gt_left">Midterm 2</td>
<td class="gt_row gt_right">20%</td></tr>
    <tr><td class="gt_row gt_left" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">Final</td>
<td class="gt_row gt_right" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">20%</td></tr>
  </tbody>
  
  
</table>
</div>

---
# Expectations for Students
	
.subheader.coral[Homework & R Homework]

- Weekly homeworks are assigned, the best way to learn mathematics is .bf[practice, practice, practice]
- Absolutely NO late homework; will drop the lowest two homeworks and the lowest R homework.
		
---
# Expectations for Students

.subheader.coral[Attendance]
		      	
- Really important to attend lecture to get handle on new material, but no attendance will be taken.
- Clicker questions will count for extra credit
            
---
# Expectations for Students

.subheader.coral[Recitation]
            
- Recitation attendance is not mandatory, but if you are going to study for 1 hour/week, recitation is the best place to do it. You will walk through examples and really helpful for prepping for exams
            
	
---
# Expectations for Students
	
.subheader.coral[R Project]
            
                
- You will download real world data and perform basic statistical analysis and create data visualizations.
             
---
# Expectations for Students

.subheader.coral[Midterms and Final Exam]
            
- NO makeup midterms, weight of missed midterm will be added to final
		      	
- Must inform me of any accommodations .bf[two weeks] before an exam
            
	
---
# What is Statistics?

.hi.purple[Statistics gives us a way of linking .it[economic theory] with the real world through data analysis]

- How did the market react when interest rates went up?

- How did firms respond to a new government policy?
		      
.hi.cranberry[Statistics allows us to translate datasets into .it[usable] information]
		      
- Summary statistics help describe large groups of data

- Use statistics to make predictions

- Statistics helps us inform our decision making

---
# Real-world examples

.subheader.coral[Coronavirus Tracking]
    
<img src="data:image/png;base64,#coronavirus.png" width="90%" style="display: block; margin: auto;" />

---
# Real-world examples

.subheader.coral[Weather Prediction]

---
# Real-world examples

.subheader.coral[Climate Change]

---
# Real-world examples

.subheader.coral[Election Predictions]

---
# Real-world examples

.subheader.coral[Election Predictions]

---
# Real-world examples

.subheader.coral[Election Predictions]

---
# Other uses of Statistics
	
.hi.purple[Statistics is used in a variety of different ways/fields]
	
		
- Financial markets
		
- Science/medical research
		
- Purchasing insurance --- how risky are you to insure?
		
- Sports -- who do you draft?

---
class: inverse, middle

# Chapter 1: Picturing Distributions with Graphs

---
# Statistics
    
        
.hi.kelly[Statistics]: the science of data. Deals with the collection, organization, analysis, interpretation and presentation of data
        
- Use statistics to identify patterns and trends in the data in order to inform decision-making
    
    
.hi.cranberry[Observation]: an individual unit of analysis in the dataset
        
- .ex[.hi.slate[Examples]: person, state, country, etc.]
        
.hi.coral[Variable]: characteristic of an observation
        
            
- .ex[.hi.slate[Examples]: age, population, GDP, etc.]

---
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<td class="gt_row gt_left">Point Guard</td>
<td class="gt_row gt_left">Golden State Warriors</td>
<td class="gt_row gt_right">40200000</td>
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<td class="gt_row gt_right">38500000</td>
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<td class="gt_row gt_right">38200000</td>
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<td class="gt_row gt_left" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">Brooklyn Nets</td>
<td class="gt_row gt_right" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">37200000</td>
<td class="gt_row gt_left" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">4 years</td></tr>
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</table>
</div>

---
# Type of Variables
    
        
.pull-left[
.hi.cranberry[Categorical variable]: takes on a unique value for each possible category or trait
            
- .ex[.hi.slate[Examples]: race, political party, dog breed, etc.]
]
.pull-right[
.hi.kelly[Quantitative variable]: measured on a numeric scale
            
- ex[.hi.slate[Examples]: income, unemployment rate, weight, etc.]
- Variables may be either .hi[discrete] (countable) or .hi[continuous] (uncountable)
]

---
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  padding: 0.5px;
  color: #333333;
  background-color: #FFFFFF;
  font-size: 80%;
  font-weight: bolder;
  border-top-style: solid;
  border-top-width: 2px;
  border-top-color: #D3D3D3;
  border-bottom-style: solid;
  border-bottom-width: 2px;
  border-bottom-color: #D3D3D3;
  vertical-align: middle;
}

#xxlojcbzts .gt_from_md > :first-child {
  margin-top: 0;
}

#xxlojcbzts .gt_from_md > :last-child {
  margin-bottom: 0;
}

#xxlojcbzts .gt_row {
  padding-top: 5px;
  padding-bottom: 5px;
  padding-left: 5px;
  padding-right: 5px;
  margin: 10px;
  border-top-style: solid;
  border-top-width: 1px;
  border-top-color: #D3D3D3;
  border-left-style: none;
  border-left-width: 1px;
  border-left-color: #D3D3D3;
  border-right-style: none;
  border-right-width: 1px;
  border-right-color: #D3D3D3;
  vertical-align: middle;
  overflow-x: hidden;
}

#xxlojcbzts .gt_stub {
  color: #333333;
  background-color: #FFFFFF;
  font-size: 80%;
  font-weight: bolder;
  text-transform: uppercase;
  border-right-style: solid;
  border-right-width: 2px;
  border-right-color: #D3D3D3;
  padding-left: 12px;
}

#xxlojcbzts .gt_summary_row {
  color: #333333;
  background-color: #FFFFFF;
  text-transform: inherit;
  padding-top: 8px;
  padding-bottom: 8px;
  padding-left: 5px;
  padding-right: 5px;
}

#xxlojcbzts .gt_first_summary_row {
  padding-top: 8px;
  padding-bottom: 8px;
  padding-left: 5px;
  padding-right: 5px;
  border-top-style: solid;
  border-top-width: 2px;
  border-top-color: #D3D3D3;
}

#xxlojcbzts .gt_grand_summary_row {
  color: #333333;
  background-color: #FFFFFF;
  text-transform: inherit;
  padding-top: 8px;
  padding-bottom: 8px;
  padding-left: 5px;
  padding-right: 5px;
}

#xxlojcbzts .gt_first_grand_summary_row {
  padding-top: 8px;
  padding-bottom: 8px;
  padding-left: 5px;
  padding-right: 5px;
  border-top-style: double;
  border-top-width: 6px;
  border-top-color: #D3D3D3;
}

#xxlojcbzts .gt_striped {
  background-color: rgba(128, 128, 128, 0.05);
}

#xxlojcbzts .gt_table_body {
  border-top-style: solid;
  border-top-width: 2px;
  border-top-color: #D3D3D3;
  border-bottom-style: solid;
  border-bottom-width: 2px;
  border-bottom-color: #D3D3D3;
}

#xxlojcbzts .gt_footnotes {
  color: #333333;
  background-color: #FFFFFF;
  border-bottom-style: none;
  border-bottom-width: 2px;
  border-bottom-color: #D3D3D3;
  border-left-style: none;
  border-left-width: 2px;
  border-left-color: #D3D3D3;
  border-right-style: none;
  border-right-width: 2px;
  border-right-color: #D3D3D3;
}

#xxlojcbzts .gt_footnote {
  margin: 0px;
  font-size: 90%;
  padding: 4px;
}

#xxlojcbzts .gt_sourcenotes {
  color: #333333;
  background-color: #FFFFFF;
  border-bottom-style: none;
  border-bottom-width: 2px;
  border-bottom-color: #D3D3D3;
  border-left-style: none;
  border-left-width: 2px;
  border-left-color: #D3D3D3;
  border-right-style: none;
  border-right-width: 2px;
  border-right-color: #D3D3D3;
}

#xxlojcbzts .gt_sourcenote {
  font-size: 12px;
  padding: 4px;
}

#xxlojcbzts .gt_left {
  text-align: left;
}

#xxlojcbzts .gt_center {
  text-align: center;
}

#xxlojcbzts .gt_right {
  text-align: right;
  font-variant-numeric: tabular-nums;
}

#xxlojcbzts .gt_font_normal {
  font-weight: normal;
}

#xxlojcbzts .gt_font_bold {
  font-weight: bold;
}

#xxlojcbzts .gt_font_italic {
  font-style: italic;
}

#xxlojcbzts .gt_super {
  font-size: 65%;
}

#xxlojcbzts .gt_footnote_marks {
  font-style: italic;
  font-weight: normal;
  font-size: 65%;
}
</style>
<table class="gt_table">
  <thead class="gt_header">
    <tr>
      <th colspan="5" class="gt_heading gt_title gt_font_normal gt_bottom_border" style><span class='hi slate' style='display: block; margin-bottom: 8px;'>NBA Salaries</span></th>
    </tr>
    
  </thead>
  <thead class="gt_col_headings">
    <tr>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">Player Name</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">Position</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">Team</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Salary</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">Contract Length</th>
    </tr>
  </thead>
  <tbody class="gt_table_body">
    <tr><td class="gt_row gt_left">Stephen Curry</td>
<td class="gt_row gt_left">Point Guard</td>
<td class="gt_row gt_left">Golden State Warriors</td>
<td class="gt_row gt_right">40200000</td>
<td class="gt_row gt_left">5 years</td></tr>
    <tr><td class="gt_row gt_left">Russell Westbrook</td>
<td class="gt_row gt_left">Point Guard</td>
<td class="gt_row gt_left">Houston Rockets</td>
<td class="gt_row gt_right">38500000</td>
<td class="gt_row gt_left">5 years</td></tr>
    <tr><td class="gt_row gt_left">Chris Paul</td>
<td class="gt_row gt_left">Point Guard</td>
<td class="gt_row gt_left">Oklahoma City Thunder</td>
<td class="gt_row gt_right">38500000</td>
<td class="gt_row gt_left">4 years</td></tr>
    <tr><td class="gt_row gt_left">Lebron James</td>
<td class="gt_row gt_left">Small Forward</td>
<td class="gt_row gt_left">Los Angeles Lakers</td>
<td class="gt_row gt_right">37400000</td>
<td class="gt_row gt_left">4 years</td></tr>
    <tr><td class="gt_row gt_left">James Harden</td>
<td class="gt_row gt_left">Shooting Guard</td>
<td class="gt_row gt_left">Houston Rockets</td>
<td class="gt_row gt_right">38200000</td>
<td class="gt_row gt_left">4 years</td></tr>
    <tr><td class="gt_row gt_left" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">Kevin Durant</td>
<td class="gt_row gt_left" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">Small Forward</td>
<td class="gt_row gt_left" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">Brooklyn Nets</td>
<td class="gt_row gt_right" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">37200000</td>
<td class="gt_row gt_left" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">4 years</td></tr>
  </tbody>
  
  
</table>
</div>

---
# Clicker Question
    
Given the following dataset, which of these statements is correct?

<div id="vaimlzpbsr" style="overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
<style>@import url("https://fonts.googleapis.com/css2?family=Chivo:ital,wght@0,100;0,200;0,300;0,400;0,500;0,600;0,700;0,800;0,900;1,100;1,200;1,300;1,400;1,500;1,600;1,700;1,800;1,900&display=swap");
html {
  font-family: Chivo, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen, Ubuntu, Cantarell, 'Helvetica Neue', 'Fira Sans', 'Droid Sans', Arial, sans-serif;
}

#vaimlzpbsr .gt_table {
  display: table;
  border-collapse: collapse;
  margin-left: auto;
  margin-right: auto;
  color: #333333;
  font-size: 16px;
  font-weight: normal;
  font-style: normal;
  background-color: #FFFFFF;
  width: auto;
  border-top-style: solid;
  border-top-width: 3px;
  border-top-color: transparent;
  border-right-style: none;
  border-right-width: 2px;
  border-right-color: #D3D3D3;
  border-bottom-style: solid;
  border-bottom-width: 3px;
  border-bottom-color: transparent;
  border-left-style: none;
  border-left-width: 2px;
  border-left-color: #D3D3D3;
}

#vaimlzpbsr .gt_heading {
  background-color: #FFFFFF;
  text-align: left;
  border-bottom-color: #FFFFFF;
  border-left-style: none;
  border-left-width: 1px;
  border-left-color: #D3D3D3;
  border-right-style: none;
  border-right-width: 1px;
  border-right-color: #D3D3D3;
}

#vaimlzpbsr .gt_title {
  color: #333333;
  font-size: 125%;
  font-weight: initial;
  padding-top: 4px;
  padding-bottom: 4px;
  border-bottom-color: #FFFFFF;
  border-bottom-width: 0;
}

#vaimlzpbsr .gt_subtitle {
  color: #333333;
  font-size: 85%;
  font-weight: initial;
  padding-top: 0;
  padding-bottom: 4px;
  border-top-color: #FFFFFF;
  border-top-width: 0;
}

#vaimlzpbsr .gt_bottom_border {
  border-bottom-style: solid;
  border-bottom-width: 2px;
  border-bottom-color: #D3D3D3;
}

#vaimlzpbsr .gt_col_headings {
  border-top-style: solid;
  border-top-width: 3px;
  border-top-color: transparent;
  border-bottom-style: solid;
  border-bottom-width: 3px;
  border-bottom-color: black;
  border-left-style: none;
  border-left-width: 1px;
  border-left-color: #D3D3D3;
  border-right-style: none;
  border-right-width: 1px;
  border-right-color: #D3D3D3;
}

#vaimlzpbsr .gt_col_heading {
  color: #333333;
  background-color: white;
  font-size: 80%;
  font-weight: bolder;
  text-transform: uppercase;
  border-left-style: none;
  border-left-width: 1px;
  border-left-color: #D3D3D3;
  border-right-style: none;
  border-right-width: 1px;
  border-right-color: #D3D3D3;
  vertical-align: bottom;
  padding-top: 5px;
  padding-bottom: 6px;
  padding-left: 5px;
  padding-right: 5px;
  overflow-x: hidden;
}

#vaimlzpbsr .gt_column_spanner_outer {
  color: #333333;
  background-color: white;
  font-size: 80%;
  font-weight: bolder;
  text-transform: uppercase;
  padding-top: 0;
  padding-bottom: 0;
  padding-left: 4px;
  padding-right: 4px;
}

#vaimlzpbsr .gt_column_spanner_outer:first-child {
  padding-left: 0;
}

#vaimlzpbsr .gt_column_spanner_outer:last-child {
  padding-right: 0;
}

#vaimlzpbsr .gt_column_spanner {
  border-bottom-style: solid;
  border-bottom-width: 3px;
  border-bottom-color: black;
  vertical-align: bottom;
  padding-top: 5px;
  padding-bottom: 6px;
  overflow-x: hidden;
  display: inline-block;
  width: 100%;
}

#vaimlzpbsr .gt_group_heading {
  padding: 8px;
  color: #333333;
  background-color: #FFFFFF;
  font-size: 80%;
  font-weight: bolder;
  text-transform: uppercase;
  border-top-style: solid;
  border-top-width: 2px;
  border-top-color: #D3D3D3;
  border-bottom-style: solid;
  border-bottom-width: 2px;
  border-bottom-color: #D3D3D3;
  border-left-style: none;
  border-left-width: 1px;
  border-left-color: #D3D3D3;
  border-right-style: none;
  border-right-width: 1px;
  border-right-color: #D3D3D3;
  vertical-align: middle;
}

#vaimlzpbsr .gt_empty_group_heading {
  padding: 0.5px;
  color: #333333;
  background-color: #FFFFFF;
  font-size: 80%;
  font-weight: bolder;
  border-top-style: solid;
  border-top-width: 2px;
  border-top-color: #D3D3D3;
  border-bottom-style: solid;
  border-bottom-width: 2px;
  border-bottom-color: #D3D3D3;
  vertical-align: middle;
}

#vaimlzpbsr .gt_from_md > :first-child {
  margin-top: 0;
}

#vaimlzpbsr .gt_from_md > :last-child {
  margin-bottom: 0;
}

#vaimlzpbsr .gt_row {
  padding-top: 5px;
  padding-bottom: 5px;
  padding-left: 5px;
  padding-right: 5px;
  margin: 10px;
  border-top-style: solid;
  border-top-width: 1px;
  border-top-color: #D3D3D3;
  border-left-style: none;
  border-left-width: 1px;
  border-left-color: #D3D3D3;
  border-right-style: none;
  border-right-width: 1px;
  border-right-color: #D3D3D3;
  vertical-align: middle;
  overflow-x: hidden;
}

#vaimlzpbsr .gt_stub {
  color: #333333;
  background-color: #FFFFFF;
  font-size: 80%;
  font-weight: bolder;
  text-transform: uppercase;
  border-right-style: solid;
  border-right-width: 2px;
  border-right-color: #D3D3D3;
  padding-left: 12px;
}

#vaimlzpbsr .gt_summary_row {
  color: #333333;
  background-color: #FFFFFF;
  text-transform: inherit;
  padding-top: 8px;
  padding-bottom: 8px;
  padding-left: 5px;
  padding-right: 5px;
}

#vaimlzpbsr .gt_first_summary_row {
  padding-top: 8px;
  padding-bottom: 8px;
  padding-left: 5px;
  padding-right: 5px;
  border-top-style: solid;
  border-top-width: 2px;
  border-top-color: #D3D3D3;
}

#vaimlzpbsr .gt_grand_summary_row {
  color: #333333;
  background-color: #FFFFFF;
  text-transform: inherit;
  padding-top: 8px;
  padding-bottom: 8px;
  padding-left: 5px;
  padding-right: 5px;
}

#vaimlzpbsr .gt_first_grand_summary_row {
  padding-top: 8px;
  padding-bottom: 8px;
  padding-left: 5px;
  padding-right: 5px;
  border-top-style: double;
  border-top-width: 6px;
  border-top-color: #D3D3D3;
}

#vaimlzpbsr .gt_striped {
  background-color: rgba(128, 128, 128, 0.05);
}

#vaimlzpbsr .gt_table_body {
  border-top-style: solid;
  border-top-width: 2px;
  border-top-color: #D3D3D3;
  border-bottom-style: solid;
  border-bottom-width: 2px;
  border-bottom-color: #D3D3D3;
}

#vaimlzpbsr .gt_footnotes {
  color: #333333;
  background-color: #FFFFFF;
  border-bottom-style: none;
  border-bottom-width: 2px;
  border-bottom-color: #D3D3D3;
  border-left-style: none;
  border-left-width: 2px;
  border-left-color: #D3D3D3;
  border-right-style: none;
  border-right-width: 2px;
  border-right-color: #D3D3D3;
}

#vaimlzpbsr .gt_footnote {
  margin: 0px;
  font-size: 90%;
  padding: 4px;
}

#vaimlzpbsr .gt_sourcenotes {
  color: #333333;
  background-color: #FFFFFF;
  border-bottom-style: none;
  border-bottom-width: 2px;
  border-bottom-color: #D3D3D3;
  border-left-style: none;
  border-left-width: 2px;
  border-left-color: #D3D3D3;
  border-right-style: none;
  border-right-width: 2px;
  border-right-color: #D3D3D3;
}

#vaimlzpbsr .gt_sourcenote {
  font-size: 12px;
  padding: 4px;
}

#vaimlzpbsr .gt_left {
  text-align: left;
}

#vaimlzpbsr .gt_center {
  text-align: center;
}

#vaimlzpbsr .gt_right {
  text-align: right;
  font-variant-numeric: tabular-nums;
}

#vaimlzpbsr .gt_font_normal {
  font-weight: normal;
}

#vaimlzpbsr .gt_font_bold {
  font-weight: bold;
}

#vaimlzpbsr .gt_font_italic {
  font-style: italic;
}

#vaimlzpbsr .gt_super {
  font-size: 65%;
}

#vaimlzpbsr .gt_footnote_marks {
  font-style: italic;
  font-weight: normal;
  font-size: 65%;
}
</style>
<table class="gt_table">
  <thead class="gt_header">
    <tr>
      <th colspan="5" class="gt_heading gt_title gt_font_normal gt_bottom_border" style><span class='hi slate' style='display: block; margin-bottom: 8px;'>Statwide Electricity Stats</span></th>
    </tr>
    
  </thead>
  <thead class="gt_col_headings">
    <tr>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">State</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Year</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Electricity Sales</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">Government</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Renewable Capacity (MWh)</th>
    </tr>
  </thead>
  <tbody class="gt_table_body">
    <tr><td class="gt_row gt_left">AK</td>
<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$5M</td>
<td class="gt_row gt_left">D</td>
<td class="gt_row gt_right">0</td></tr>
    <tr><td class="gt_row gt_left">AL</td>
<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$77M</td>
<td class="gt_row gt_left">D</td>
<td class="gt_row gt_right">493</td></tr>
    <tr><td class="gt_row gt_left">AR</td>
<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$36M</td>
<td class="gt_row gt_left">R</td>
<td class="gt_row gt_right">369</td></tr>
    <tr><td class="gt_row gt_left">AZ</td>
<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$64M</td>
<td class="gt_row gt_left">R</td>
<td class="gt_row gt_right">1</td></tr>
    <tr><td class="gt_row gt_left">CA</td>
<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$220M</td>
<td class="gt_row gt_left">D</td>
<td class="gt_row gt_right">3053</td></tr>
    <tr><td class="gt_row gt_left">CO</td>
<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$47M</td>
<td class="gt_row gt_left">R</td>
<td class="gt_row gt_right">29</td></tr>
    <tr><td class="gt_row gt_left" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">CT</td>
<td class="gt_row gt_right" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">2000</td>
<td class="gt_row gt_right" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">$34M</td>
<td class="gt_row gt_left" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">R</td>
<td class="gt_row gt_right" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">262</td></tr>
  </tbody>
  
  
</table>
</div>

<ol type="a">       
	<li>Electricity sales, renewable capacity and state are all quantitative variables</li>
	<li>Government, state are both categorical variables</li>
	<li>All variables are categorical</li>
	<li>All variables are quantitative</li>
</ol>

---
# Dummy Variables
    
Often time in datasets .hi.purple[dummy variables], or .it[indicator variables], are used to describe categorical variables.

- .ex[.hi.slate[Example]: the "Government" variable as 0 for D and 1 for R.]

Sometimes Dummy/indicator variables put observations into categories, even though they are numerical in value
    
- .ex[.hi.slate[Example]: Years of schooling into "HS Degree" dummy (years $ >12 $)]

---
# Distribution of a Variable
    
        
.hi.kelly[Distribution of a variable]: tells us .it[what values] it takes and .it[how often] it takes these values
            
              
- lists all possible outcomes of variable and their associated frequencies

<div id="svyvfwrzfr" style="overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
<style>@import url("https://fonts.googleapis.com/css2?family=Chivo:ital,wght@0,100;0,200;0,300;0,400;0,500;0,600;0,700;0,800;0,900;1,100;1,200;1,300;1,400;1,500;1,600;1,700;1,800;1,900&display=swap");
html {
  font-family: Chivo, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen, Ubuntu, Cantarell, 'Helvetica Neue', 'Fira Sans', 'Droid Sans', Arial, sans-serif;
}

#svyvfwrzfr .gt_table {
  display: table;
  border-collapse: collapse;
  margin-left: auto;
  margin-right: auto;
  color: #333333;
  font-size: 16px;
  font-weight: normal;
  font-style: normal;
  background-color: #FFFFFF;
  width: auto;
  border-top-style: solid;
  border-top-width: 3px;
  border-top-color: transparent;
  border-right-style: none;
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      <th colspan="5" class="gt_heading gt_title gt_font_normal gt_bottom_border" style><span class='hi slate' style='display: block; margin-bottom: 8px;'>Statwide Electricity Stats</span></th>
    </tr>
    
  </thead>
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      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">State</th>
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    <tr><td class="gt_row gt_left">AK</td>
<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$5M</td>
<td class="gt_row gt_left">D</td>
<td class="gt_row gt_right">0</td></tr>
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<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$77M</td>
<td class="gt_row gt_left">D</td>
<td class="gt_row gt_right">493</td></tr>
    <tr><td class="gt_row gt_left">AR</td>
<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$36M</td>
<td class="gt_row gt_left">R</td>
<td class="gt_row gt_right">369</td></tr>
    <tr><td class="gt_row gt_left">AZ</td>
<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$64M</td>
<td class="gt_row gt_left">R</td>
<td class="gt_row gt_right">1</td></tr>
    <tr><td class="gt_row gt_left">CA</td>
<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$220M</td>
<td class="gt_row gt_left">D</td>
<td class="gt_row gt_right">3053</td></tr>
    <tr><td class="gt_row gt_left">CO</td>
<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$47M</td>
<td class="gt_row gt_left">R</td>
<td class="gt_row gt_right">29</td></tr>
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<td class="gt_row gt_right" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">2000</td>
<td class="gt_row gt_right" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">$34M</td>
<td class="gt_row gt_left" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">R</td>
<td class="gt_row gt_right" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">262</td></tr>
  </tbody>
  
  
</table>
</div>

What is the distribution of Government?

---
# Distribution of a Variable

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      <th colspan="5" class="gt_heading gt_title gt_font_normal gt_bottom_border" style><span class='hi slate' style='display: block; margin-bottom: 8px;'>Statwide Electricity Stats</span></th>
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      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">State</th>
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    <tr><td class="gt_row gt_left">AK</td>
<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$5M</td>
<td class="gt_row gt_center"><span class='hi kelly'>D</span></td>
<td class="gt_row gt_right">0</td></tr>
    <tr><td class="gt_row gt_left">AL</td>
<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$77M</td>
<td class="gt_row gt_center"><span class='hi kelly'>D</span></td>
<td class="gt_row gt_right">493</td></tr>
    <tr><td class="gt_row gt_left">AR</td>
<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$36M</td>
<td class="gt_row gt_center"><span class='hi kelly'>R</span></td>
<td class="gt_row gt_right">369</td></tr>
    <tr><td class="gt_row gt_left">AZ</td>
<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$64M</td>
<td class="gt_row gt_center"><span class='hi kelly'>R</span></td>
<td class="gt_row gt_right">1</td></tr>
    <tr><td class="gt_row gt_left">CA</td>
<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$220M</td>
<td class="gt_row gt_center"><span class='hi kelly'>D</span></td>
<td class="gt_row gt_right">3053</td></tr>
    <tr><td class="gt_row gt_left">CO</td>
<td class="gt_row gt_right">2000</td>
<td class="gt_row gt_right">$47M</td>
<td class="gt_row gt_center"><span class='hi kelly'>R</span></td>
<td class="gt_row gt_right">29</td></tr>
    <tr><td class="gt_row gt_left" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">CT</td>
<td class="gt_row gt_right" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">2000</td>
<td class="gt_row gt_right" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">$34M</td>
<td class="gt_row gt_center" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;"><span class='hi kelly'>R</span></td>
<td class="gt_row gt_right" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">262</td></tr>
  </tbody>
  
  
</table>
</div>

.hi[Distribution of Government]:
.cranberry[D] - 3/7 and .kelly[R] - 4/7

---
# Visualizing Categorical Variable
    
        
Distribution of categorical variable lists the categories and gives .hi[the count/percent] of individuals who fall into each category.
        
- Often visualize distributions of categorical variables using .hi[pie charts] or .hi[bar graphs].

---
# Examples

<div id="kxyvcvbuwr" style="overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
<style>@import url("https://fonts.googleapis.com/css2?family=Chivo:ital,wght@0,100;0,200;0,300;0,400;0,500;0,600;0,700;0,800;0,900;1,100;1,200;1,300;1,400;1,500;1,600;1,700;1,800;1,900&display=swap");
html {
  font-family: Chivo, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen, Ubuntu, Cantarell, 'Helvetica Neue', 'Fira Sans', 'Droid Sans', Arial, sans-serif;
}

#kxyvcvbuwr .gt_table {
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  width: auto;
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  border-top-width: 3px;
  border-top-color: transparent;
  border-right-style: none;
  border-right-width: 2px;
  border-right-color: #D3D3D3;
  border-bottom-style: solid;
  border-bottom-width: 3px;
  border-bottom-color: transparent;
  border-left-style: none;
  border-left-width: 2px;
  border-left-color: #D3D3D3;
}

#kxyvcvbuwr .gt_heading {
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  border-right-color: #D3D3D3;
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#kxyvcvbuwr .gt_title {
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  font-weight: initial;
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  padding-bottom: 4px;
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  font-size: 85%;
  font-weight: initial;
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  padding-bottom: 4px;
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  border-top-width: 0;
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#kxyvcvbuwr .gt_bottom_border {
  border-bottom-style: solid;
  border-bottom-width: 2px;
  border-bottom-color: #D3D3D3;
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#kxyvcvbuwr .gt_col_headings {
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  border-top-width: 3px;
  border-top-color: transparent;
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  border-left-width: 1px;
  border-left-color: #D3D3D3;
  border-right-style: none;
  border-right-width: 1px;
  border-right-color: #D3D3D3;
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#kxyvcvbuwr .gt_col_heading {
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  background-color: white;
  font-size: 80%;
  font-weight: bolder;
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  border-right-color: #D3D3D3;
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  padding-bottom: 6px;
  padding-left: 5px;
  padding-right: 5px;
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#kxyvcvbuwr .gt_column_spanner_outer {
  color: #333333;
  background-color: white;
  font-size: 80%;
  font-weight: bolder;
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  padding-bottom: 0;
  padding-left: 4px;
  padding-right: 4px;
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#kxyvcvbuwr .gt_column_spanner_outer:first-child {
  padding-left: 0;
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#kxyvcvbuwr .gt_column_spanner_outer:last-child {
  padding-right: 0;
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#kxyvcvbuwr .gt_column_spanner {
  border-bottom-style: solid;
  border-bottom-width: 3px;
  border-bottom-color: black;
  vertical-align: bottom;
  padding-top: 5px;
  padding-bottom: 6px;
  overflow-x: hidden;
  display: inline-block;
  width: 100%;
}

#kxyvcvbuwr .gt_group_heading {
  padding: 8px;
  color: #333333;
  background-color: #FFFFFF;
  font-size: 80%;
  font-weight: bolder;
  text-transform: uppercase;
  border-top-style: solid;
  border-top-width: 2px;
  border-top-color: #D3D3D3;
  border-bottom-style: solid;
  border-bottom-width: 2px;
  border-bottom-color: #D3D3D3;
  border-left-style: none;
  border-left-width: 1px;
  border-left-color: #D3D3D3;
  border-right-style: none;
  border-right-width: 1px;
  border-right-color: #D3D3D3;
  vertical-align: middle;
}

#kxyvcvbuwr .gt_empty_group_heading {
  padding: 0.5px;
  color: #333333;
  background-color: #FFFFFF;
  font-size: 80%;
  font-weight: bolder;
  border-top-style: solid;
  border-top-width: 2px;
  border-top-color: #D3D3D3;
  border-bottom-style: solid;
  border-bottom-width: 2px;
  border-bottom-color: #D3D3D3;
  vertical-align: middle;
}

#kxyvcvbuwr .gt_from_md > :first-child {
  margin-top: 0;
}

#kxyvcvbuwr .gt_from_md > :last-child {
  margin-bottom: 0;
}

#kxyvcvbuwr .gt_row {
  padding-top: 5px;
  padding-bottom: 5px;
  padding-left: 5px;
  padding-right: 5px;
  margin: 10px;
  border-top-style: solid;
  border-top-width: 1px;
  border-top-color: #D3D3D3;
  border-left-style: none;
  border-left-width: 1px;
  border-left-color: #D3D3D3;
  border-right-style: none;
  border-right-width: 1px;
  border-right-color: #D3D3D3;
  vertical-align: middle;
  overflow-x: hidden;
}

#kxyvcvbuwr .gt_stub {
  color: #333333;
  background-color: #FFFFFF;
  font-size: 80%;
  font-weight: bolder;
  text-transform: uppercase;
  border-right-style: solid;
  border-right-width: 2px;
  border-right-color: #D3D3D3;
  padding-left: 12px;
}

#kxyvcvbuwr .gt_summary_row {
  color: #333333;
  background-color: #FFFFFF;
  text-transform: inherit;
  padding-top: 8px;
  padding-bottom: 8px;
  padding-left: 5px;
  padding-right: 5px;
}

#kxyvcvbuwr .gt_first_summary_row {
  padding-top: 8px;
  padding-bottom: 8px;
  padding-left: 5px;
  padding-right: 5px;
  border-top-style: solid;
  border-top-width: 2px;
  border-top-color: #D3D3D3;
}

#kxyvcvbuwr .gt_grand_summary_row {
  color: #333333;
  background-color: #FFFFFF;
  text-transform: inherit;
  padding-top: 8px;
  padding-bottom: 8px;
  padding-left: 5px;
  padding-right: 5px;
}

#kxyvcvbuwr .gt_first_grand_summary_row {
  padding-top: 8px;
  padding-bottom: 8px;
  padding-left: 5px;
  padding-right: 5px;
  border-top-style: double;
  border-top-width: 6px;
  border-top-color: #D3D3D3;
}

#kxyvcvbuwr .gt_striped {
  background-color: rgba(128, 128, 128, 0.05);
}

#kxyvcvbuwr .gt_table_body {
  border-top-style: solid;
  border-top-width: 2px;
  border-top-color: #D3D3D3;
  border-bottom-style: solid;
  border-bottom-width: 2px;
  border-bottom-color: #D3D3D3;
}

#kxyvcvbuwr .gt_footnotes {
  color: #333333;
  background-color: #FFFFFF;
  border-bottom-style: none;
  border-bottom-width: 2px;
  border-bottom-color: #D3D3D3;
  border-left-style: none;
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  border-right-width: 2px;
  border-right-color: #D3D3D3;
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#kxyvcvbuwr .gt_footnote {
  margin: 0px;
  font-size: 90%;
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#kxyvcvbuwr .gt_sourcenotes {
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#kxyvcvbuwr .gt_sourcenote {
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#kxyvcvbuwr .gt_left {
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#kxyvcvbuwr .gt_center {
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  text-align: right;
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  font-weight: normal;
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#kxyvcvbuwr .gt_font_bold {
  font-weight: bold;
}

#kxyvcvbuwr .gt_font_italic {
  font-style: italic;
}

#kxyvcvbuwr .gt_super {
  font-size: 65%;
}

#kxyvcvbuwr .gt_footnote_marks {
  font-style: italic;
  font-weight: normal;
  font-size: 65%;
}
</style>
<table class="gt_table">
  <thead class="gt_header">
    <tr>
      <th colspan="2" class="gt_heading gt_title gt_font_normal gt_bottom_border" style><span class='hi slate' style='display: block; margin-bottom: 8px;'>Distribution of CU Boulder Students</span></th>
    </tr>
    
  </thead>
  <thead class="gt_col_headings">
    <tr>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">Field of Study</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Percent of Students</th>
    </tr>
  </thead>
  <tbody class="gt_table_body">
    <tr><td class="gt_row gt_left">Arts and Humanities</td>
<td class="gt_row gt_right">10.1%</td></tr>
    <tr><td class="gt_row gt_left">Biological Sciences</td>
<td class="gt_row gt_right">14.9%</td></tr>
    <tr><td class="gt_row gt_left">Business</td>
<td class="gt_row gt_right">13.4%</td></tr>
    <tr><td class="gt_row gt_left">Education</td>
<td class="gt_row gt_right">4.2%</td></tr>
    <tr><td class="gt_row gt_left">Engineering</td>
<td class="gt_row gt_right">13.1%</td></tr>
    <tr><td class="gt_row gt_left">Health Professions</td>
<td class="gt_row gt_right">11.3%</td></tr>
    <tr><td class="gt_row gt_left">Math and Computer Science</td>
<td class="gt_row gt_right">5.4%</td></tr>
    <tr><td class="gt_row gt_left">Physical Sciences</td>
<td class="gt_row gt_right">10.8%</td></tr>
    <tr><td class="gt_row gt_left" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">Other majors</td>
<td class="gt_row gt_right" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">13.9%</td></tr>
  </tbody>
  
  
</table>
</div>

---
# Examples

.pull-left[
.hi[Pie Chart]

<img src="data:image/png;base64,#ch1_files/figure-html/pie-chart-1.svg" style="display: block; margin: auto;" />
	
]
.pull-right[
.hi[Bar Chart]
<img src="data:image/png;base64,#ch1_files/figure-html/bar-chart-1.svg" style="display: block; margin: auto;" />
]

---
# Visualizing Continuous Variable
    
.hi.kelly[Distribution of a variable]: tells us .it[what values] it takes and .it[how often] it takes these values
        
- Often visualize distributions of continuous variables using .hi[histograms], .hi[stemplots], or .hi[time plots] if variable is measured over time

---
# Histogram
    
- A .hi.purple[histogram] shows the distribution of a continuous variable by using bars whose height represents number of individuals who take on a value within a particular .kelly[interval (bin)]

- Appropriate for variables that take on many different values or have large number of observations

- To make a histogram:

- Divide the possible values into .kelly[intervals (bins)] of equal widths
        
	- Count how many observations fall into each .kelly[interval (bin)]
        
	- For each interval, draw a bar whose .cranberry[height] is equivalent to the number (or percent) of observations in each interval

---
class: clear,middle

<div id="zyhpwnezxq" style="overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
<style>@import url("https://fonts.googleapis.com/css2?family=Chivo:ital,wght@0,100;0,200;0,300;0,400;0,500;0,600;0,700;0,800;0,900;1,100;1,200;1,300;1,400;1,500;1,600;1,700;1,800;1,900&display=swap");
html {
  font-family: Chivo, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen, Ubuntu, Cantarell, 'Helvetica Neue', 'Fira Sans', 'Droid Sans', Arial, sans-serif;
}

#zyhpwnezxq .gt_table {
  display: table;
  border-collapse: collapse;
  margin-left: auto;
  margin-right: auto;
  color: #333333;
  font-size: 16px;
  font-weight: normal;
  font-style: normal;
  background-color: #FFFFFF;
  width: auto;
  border-top-style: solid;
  border-top-width: 3px;
  border-top-color: transparent;
  border-right-style: none;
  border-right-width: 2px;
  border-right-color: #D3D3D3;
  border-bottom-style: solid;
  border-bottom-width: 3px;
  border-bottom-color: transparent;
  border-left-style: none;
  border-left-width: 2px;
  border-left-color: #D3D3D3;
}

#zyhpwnezxq .gt_heading {
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  text-align: left;
  border-bottom-color: #FFFFFF;
  border-left-style: none;
  border-left-width: 1px;
  border-left-color: #D3D3D3;
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#zyhpwnezxq .gt_title {
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  font-weight: initial;
  padding-top: 4px;
  padding-bottom: 4px;
  border-bottom-color: #FFFFFF;
  border-bottom-width: 0;
}

#zyhpwnezxq .gt_subtitle {
  color: #333333;
  font-size: 85%;
  font-weight: initial;
  padding-top: 0;
  padding-bottom: 4px;
  border-top-color: #FFFFFF;
  border-top-width: 0;
}

#zyhpwnezxq .gt_bottom_border {
  border-bottom-style: solid;
  border-bottom-width: 2px;
  border-bottom-color: #D3D3D3;
}

#zyhpwnezxq .gt_col_headings {
  border-top-style: solid;
  border-top-width: 3px;
  border-top-color: transparent;
  border-bottom-style: solid;
  border-bottom-width: 3px;
  border-bottom-color: black;
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  border-left-color: #D3D3D3;
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#zyhpwnezxq .gt_col_heading {
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  font-size: 80%;
  font-weight: bolder;
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  border-left-width: 1px;
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  border-right-width: 1px;
  border-right-color: #D3D3D3;
  vertical-align: bottom;
  padding-top: 5px;
  padding-bottom: 6px;
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#zyhpwnezxq .gt_column_spanner_outer {
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  background-color: white;
  font-size: 80%;
  font-weight: bolder;
  text-transform: uppercase;
  padding-top: 0;
  padding-bottom: 0;
  padding-left: 4px;
  padding-right: 4px;
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#zyhpwnezxq .gt_column_spanner_outer:first-child {
  padding-left: 0;
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#zyhpwnezxq .gt_column_spanner_outer:last-child {
  padding-right: 0;
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#zyhpwnezxq .gt_column_spanner {
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  vertical-align: bottom;
  padding-top: 5px;
  padding-bottom: 6px;
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  display: inline-block;
  width: 100%;
}

#zyhpwnezxq .gt_group_heading {
  padding: 8px;
  color: #333333;
  background-color: #FFFFFF;
  font-size: 80%;
  font-weight: bolder;
  text-transform: uppercase;
  border-top-style: solid;
  border-top-width: 2px;
  border-top-color: #D3D3D3;
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  border-right-width: 1px;
  border-right-color: #D3D3D3;
  vertical-align: middle;
}

#zyhpwnezxq .gt_empty_group_heading {
  padding: 0.5px;
  color: #333333;
  background-color: #FFFFFF;
  font-size: 80%;
  font-weight: bolder;
  border-top-style: solid;
  border-top-width: 2px;
  border-top-color: #D3D3D3;
  border-bottom-style: solid;
  border-bottom-width: 2px;
  border-bottom-color: #D3D3D3;
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#zyhpwnezxq .gt_from_md > :first-child {
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#zyhpwnezxq .gt_from_md > :last-child {
  margin-bottom: 0;
}

#zyhpwnezxq .gt_row {
  padding-top: 5px;
  padding-bottom: 5px;
  padding-left: 5px;
  padding-right: 5px;
  margin: 10px;
  border-top-style: solid;
  border-top-width: 1px;
  border-top-color: #D3D3D3;
  border-left-style: none;
  border-left-width: 1px;
  border-left-color: #D3D3D3;
  border-right-style: none;
  border-right-width: 1px;
  border-right-color: #D3D3D3;
  vertical-align: middle;
  overflow-x: hidden;
}

#zyhpwnezxq .gt_stub {
  color: #333333;
  background-color: #FFFFFF;
  font-size: 80%;
  font-weight: bolder;
  text-transform: uppercase;
  border-right-style: solid;
  border-right-width: 2px;
  border-right-color: #D3D3D3;
  padding-left: 12px;
}

#zyhpwnezxq .gt_summary_row {
  color: #333333;
  background-color: #FFFFFF;
  text-transform: inherit;
  padding-top: 8px;
  padding-bottom: 8px;
  padding-left: 5px;
  padding-right: 5px;
}

#zyhpwnezxq .gt_first_summary_row {
  padding-top: 8px;
  padding-bottom: 8px;
  padding-left: 5px;
  padding-right: 5px;
  border-top-style: solid;
  border-top-width: 2px;
  border-top-color: #D3D3D3;
}

#zyhpwnezxq .gt_grand_summary_row {
  color: #333333;
  background-color: #FFFFFF;
  text-transform: inherit;
  padding-top: 8px;
  padding-bottom: 8px;
  padding-left: 5px;
  padding-right: 5px;
}

#zyhpwnezxq .gt_first_grand_summary_row {
  padding-top: 8px;
  padding-bottom: 8px;
  padding-left: 5px;
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      <th colspan="3" class="gt_heading gt_title gt_font_normal gt_bottom_border" style><span class='hi slate' style='display: block; margin-bottom: 8px;'>State-level Graduation Rates</span></th>
    </tr>
    
  </thead>
  <thead class="gt_col_headings">
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      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1"></th>
      <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">State</th>
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    <tr><td class="gt_row gt_left gt_stub" style="font-family: Courier;">1</td>
<td class="gt_row gt_left">Alabama</td>
<td class="gt_row gt_right">90.0%</td></tr>
    <tr><td class="gt_row gt_left gt_stub" style="font-family: Courier;">2</td>
<td class="gt_row gt_left">Alaska</td>
<td class="gt_row gt_right">78.5%</td></tr>
    <tr><td class="gt_row gt_left gt_stub" style="font-family: Courier;">3</td>
<td class="gt_row gt_left">Arizona</td>
<td class="gt_row gt_right">78.7%</td></tr>
    <tr><td class="gt_row gt_left gt_stub" style="font-family: Courier;">4</td>
<td class="gt_row gt_left">Arkansas</td>
<td class="gt_row gt_right">89.2%</td></tr>
    <tr><td class="gt_row gt_left gt_stub" style="font-family: Courier;">5</td>
<td class="gt_row gt_left">California</td>
<td class="gt_row gt_right">83.0%</td></tr>
    <tr><td class="gt_row gt_left gt_stub" style="font-family: Courier; font-size: x-small; background-color: #E4E4E4;">6..50</td>
<td class="gt_row gt_left" style="background-color: #E4E4E4;"></td>
<td class="gt_row gt_right" style="background-color: #E4E4E4;"></td></tr>
    <tr><td class="gt_row gt_left gt_stub" style="font-family: Courier;">51</td>
<td class="gt_row gt_left" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">Wyoming</td>
<td class="gt_row gt_right" style="border-bottom-width: 2px; border-bottom-style: solid; border-bottom-color: transparent;">81.7%</td></tr>
  </tbody>
  
  
</table>
</div>

---
# Graduation Rates

---
# Less Informative

---
# Too Many Bins

---
# Interpreting Histogram
    
        
How to interpret histograms:
        
- Look for overall pattern and striking deviations from that pattern
	- An important kind of deviation is an .hi.purple[outlier], an observation that falls .it[outside the overall pattern]

- Describe the pattern by its .hi[shape], .hi[center], and .hi[variability] (or spread)

---
# Shapes of Distributions
    
We describe the shape of the distribution as
    
        
- .hi.cranberry[symmetric]: the right and left sides of the graph are approximately mirror images of each other
        
- .hi.kelly[right-skewed]: the right side of the graph (containing the half of the observations with larger values) is much longer than the left side
        
- .hi.alice[left-skewed]: the left side of the graph is much longer than the right side

---
# Skewness Examples
    
    
<img src="data:image/png;base64,#ch1_files/figure-html/skew-1.svg" width="900" style="display: block; margin: auto;" />

---
# Clicker Question

<ol type="a" style="display: block">
	<li style="float:left; width: 200px"> symmetric </li>
	<li style="float:left; width: 200px"> left-skewed </li>
	<li style="float:left; width: 200px"> right-skewed </li>
</ol>

---
# Clicker Question
    
For which of the following variables would you need to use a histogram instead of a bar graph?

<ol type="a" style="display: block">
	<li> month of birth </li>
	<li> distance from nearest metropolitan area </li>
	<li> employment status </li>
	<li> none of the above </li>
</ol>

---
# Time Plots
    
        
.hi.purple[Time Series] is a connected line plotting the value of the variable over time
        
- Shows behavior over time which emphasizes .it[trends]

- Time is always on the .bf[horizontal] axis, variable being measured on .bf[vertical] axis

- Shows .it[trends] and .it[deviations from trends]
	- Also want to look for seasonal variation

---
# Time Series Plots

---
# Deviation from Trends